This set of Aptitude Questions and Answers (MCQs) focuses on “Spheres and Hemispheres”.
1. Which of the following is the correct formula for the volume of a sphere?
a) (4 / 9) * π * r3
b) (2 / 9) * π * r3
c) (4 / 3) * π * r3
d) (2 / 3) * π * r3
View Answer
Explanation:
Let the radius of the sphere be r.
The correct formula for the volume of a sphere of radius r = (4 / 3) * π * r3.
2. What will be the radius of a spherical vessel having a volume of 5600 cm3?
a) 11 cm
b) 12 cm
c) 9 cm
d) 13 cm
View Answer
Explanation: Given,
Volume of spherical vessel = (4 / 3) * π * r3
➩ 5600 cm3 = (4 / 3) * π * r3
➩ 5600 = (4 / 3) * (22 / 7) * r3
➩ 5600 * 3 * 7 / (4 * 22) = r3
➩ 117600 / 88 = r3
➩ 1336.36 = r3
➩ r = 11 cm
3. Which of the following is the correct option expressing the volume of a hemisphere?
a) (2 / 9) * π * r3
b) (2 / 3) * π * r3
c) (4 / 3) * π * r3
d) (4 / 9) * π * r3
View Answer
Explanation: Let the radius of the hemisphere be r.
Correct formula for the volume of a hemisphere = (2 / 3) * π * r3.
4. If two solid hemispheres of same base radii as (3 / 2) r, are joined together along their bases, then what would be the curved surface area of this new solid?
a) 9πr2
b) 12πr2
c) 16πr2
d) 6πr2
View Answer
Explanation:
Curved surface area of a solid hemisphere = 2 * π * ((3 / 2) r)2
Thus, curved surface area of new solid = 2 * (2 * π * (9 / 4) r2)
= 9πr2
5. What is the volume (in cubic cm) of a hemispherical bowl of radius 12 cm?
a) 1331π
b) 1420π
c) 1152π
d) 1519π
View Answer
Explanation: Given,
r = 12 cm
Volume of hemisphere = (2 / 3) * πr3
= (2 / 3) * π * (12)3
= 1152π
6. If the radius of a sphere is made five times, what will be the ratio of the volume of new sphere to the ratio of volume of original sphere?
a) 5:1
b) 25:1
c) 1:625
d) 125:1
View Answer
Explanation: Let the radius of original sphere = r
Volume of original sphere = (4 / 3) * πr3
Radius of new sphere = 5r
Volume of new sphere = (4 / 3) * π * (5r)3
= (4 / 3) * 125πr3
Ratio = Volume of new sphere / Volume of original sphere
= ((4 / 3) * 125πr3) / ((4 / 3) * πr3)
= 125:1
7. If the radius of a hemisphere is reduced to half, then, how many times is the volume of the new hemisphere to original hemisphere?
a) 1 / 8 times
b) 1 / 2 times
c) 1 / 4 times
d) 1 / 16 times
View Answer
Explanation: Let the side of the original hemisphere = r
Volume of original hemisphere = (2 / 3) * πr3
The side of new hemisphere = (1 / 2) r
Volume of new hemisphere = (2 / 3) * π * ((1 / 2) r)3
Thus, on comparing,
The volume of new hemisphere is (1 / 8) times the original hemisphere.
8. A hemispherical bowl has a radius of 7 cm. How much cubic cm of water will this bowl contain if its half-filled?
a) 765.46
b) 723.22
c) 718.66
d) 732.99
View Answer
Explanation: Given,
r = 7 cm
Volume of hemisphere = (2 / 3) * πr3
= (2 / 3) * (22 / 7) * (7)3
= 718.66 cm3
9. Two sphere of radius 2 cm each are melted and casted into a single sphere. What would be the radius of this new sphere?
a) 4 cm
b) 161/3 cm
c) 121/3 cm
d) 2 cm
View Answer
Explanation: Given,
r = 2 cm, let the radius of new sphere = R
According to the question
2 * ((4 / 3) * πr3) = (4 / 3) * πR3
2 * ((4 / 3) * π (2)3) = (4 / 3) * πR3
2 * 8 = R3
R = 161/3 cm
10. What will be the volume of a sphere having radius as 21 cm?
a) 38,808 cm3
b) 14,400 cm3
c) 28,562 cm3
d) 49,263 cm3
View Answer
Explanation: Given,
r = 21 cm
Volume of sphere = (4 / 3) * πr3
= (4 / 3) * (22 / 7) * (21)3
= 38,808 cm3
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